diff --git a/src/Distributions/mixture.jl b/src/Distributions/mixture.jl
index 931dafd..684f1ff 100644
--- a/src/Distributions/mixture.jl
+++ b/src/Distributions/mixture.jl
@@ -79,27 +79,27 @@ function rand(d::MixtureModel{Union{Univariate,Multivariate}, Continuous, Gibbs}
 end 
 
 # 2 - pdf
-function pdf(d::MixtureModel{Union{Univariate,Multivariate}, Continuous, Gibbs}, x::Float64, normint::Integrator)
+function pdf(d::MixtureModel{Union{Univariate,Multivariate}, Continuous, Gibbs}, x::Float64, normint::GibbsIntegrator)
     p = probs(d)
     return sum(p_i * pdf(component(d, i), x, normint) for (i, p_i) in enumerate(p) if !iszero(p_i))
 end 
 
 # multiple samples of x
-function pdf(d::MixtureModel{Union{Univariate,Multivariate}, Continuous, Gibbs}, xsamp::Vector{Float64}, normint::Integrator)
+function pdf(d::MixtureModel{Union{Univariate,Multivariate}, Continuous, Gibbs}, xsamp::Vector{Float64}, normint::GibbsIntegrator)
     p = probs(d)
     return sum(p_i * updf.((component(d, i),), xsamp) ./ normconst(component(d, i), normint) for (i, p_i) in enumerate(p) if !iszero(p_i))
 end 
 
 
 # 3 - log unnormalized pdf
-function logpdf(d::MixtureModel{Union{Univariate,Multivariate}, Continuous, Gibbs}, x::Float64, normint::Integrator)
+function logpdf(d::MixtureModel{Union{Univariate,Multivariate}, Continuous, Gibbs}, x::Float64, normint::GibbsIntegrator)
     p = probs(d)
     lp = logsumexp(log(p_i) + logpdf(component(d, i), x, normint) for (i, p_i) in enumerate(p) if !iszero(p_i))
     return lp
 end
 
 # multiple samples of x
-function logpdf(d::MixtureModel{Union{Univariate,Multivariate}, Continuous, Gibbs}, xsamp::Vector{Float64}, normint::Integrator)
+function logpdf(d::MixtureModel{Union{Univariate,Multivariate}, Continuous, Gibbs}, xsamp::Vector{Float64}, normint::GibbsIntegrator)
     p = probs(d)
     data = reduce(hcat, [log(p_i) .+ logupdf.((component(d, i),), xsamp) .- log(normconst(component(d, i), normint)) for (i, p_i) in enumerate(p) if !iszero(p_i)])
     lp = logsumexp.([data[i,:] for i = 1:size(data,1)])
diff --git a/src/Integrators/importance_sampling.jl b/src/Integrators/importance_sampling.jl
index 0e8db85..a3c9105 100644
--- a/src/Integrators/importance_sampling.jl
+++ b/src/Integrators/importance_sampling.jl
@@ -1,4 +1,4 @@
-abstract type ISIntegrator <: Integrator end
+abstract type ISIntegrator <: GibbsIntegrator end
 
 """
 struct ISMC <: ISIntegrator
@@ -44,15 +44,15 @@ This method is implemented with the user providing samples from the biasing dist
 # Arguments
 - `g :: Distribution`                               : biasing distribution
 - `xsamp :: Vector`                                 : fixed set of samples
-- `normint :: Union{Integrator, Nothing}`           : integrator for computing normalizing constant of biasing distribution (required for mixture models)
+- `normint :: Union{GibbsIntegrator, Nothing}`           : integrator for computing normalizing constant of biasing distribution (required for mixture models)
 
 """
 mutable struct ISSamples <: ISIntegrator
     g :: Distribution
     xsamp :: Vector
-    normint :: Union{Integrator, Nothing}
+    normint :: Union{GibbsIntegrator, Nothing}
 
-    function ISSamples(g::MixtureModel, xsamp::Vector, normint::Integrator)
+    function ISSamples(g::MixtureModel, xsamp::Vector, normint::GibbsIntegrator)
         return new(g, xsamp, normint)
     end
 
@@ -76,7 +76,7 @@ This method is implemented with the user providing samples from each component m
 - `n :: Int`                 : number of samples
 - `knl :: Kernel`            : kernel function to compute mixture weights
 - `xsamp :: Vector`          : Vector of sample sets from each component distribution
-- `normint :: Integrator`    : Integrator for the approximating the normalizing constant of each component distribution
+- `normint :: GibbsIntegrator`    : Integrator for the approximating the normalizing constant of each component distribution
 
 """
 mutable struct ISMixSamples <: ISIntegrator
@@ -85,14 +85,14 @@ mutable struct ISMixSamples <: ISIntegrator
     n :: Int
     knl :: Kernel
     xsamp :: Vector
-    normint :: Integrator
+    normint :: GibbsIntegrator
 
 
-    function ISMixSamples(g::MixtureModel, refs::Vector, n::Int, knl::Kernel, xsamp::Vector, normint::Integrator)
+    function ISMixSamples(g::MixtureModel, refs::Vector, n::Int, knl::Kernel, xsamp::Vector, normint::GibbsIntegrator)
         return new(g, refs, n, knl, xsamp, normint)
     end
 
-    function ISMixSamples(g::MixtureModel, n::Int, knl::Kernel, xsamp::Vector, normint::Integrator)
+    function ISMixSamples(g::MixtureModel, n::Int, knl::Kernel, xsamp::Vector, normint::GibbsIntegrator)
         d = new()
         d.g = g
         d.refs = [πg.θ for πg in g.components]
diff --git a/src/Integrators/integrators.jl b/src/Integrators/integrators.jl
index 2331a8d..d74b817 100644
--- a/src/Integrators/integrators.jl
+++ b/src/Integrators/integrators.jl
@@ -1,20 +1,31 @@
+abstract type Integrator end
 """ 
-    Integrator
+    GibbsIntegrator
 
-    A struct of abstract type Integrator computes the expectation of a function h(x, θ) with respect to an invariant measure p(x, θ).
+    A struct of abstract type GibbsIntegrator computes the expectation of a function h(x, θ) with respect to the invariant measure p(x, θ).
 """
-abstract type Integrator end
+abstract type GibbsIntegrator <: Integrator end
+
+""" 
+    PathIntegrator
+
+    A struct of abstract type PathIntegrator computes the expectation of a functional h with respect to the path measure P. 
+"""
+abstract type PathIntegrator <: Integrator end
 
 include("quadrature.jl")
 include("monte_carlo.jl")
 include("importance_sampling.jl")
+include("path_integrators.jl")
+
 
 export
-    Integrator, 
+    GibbsIntegrator, 
     MCIntegrator,
     MonteCarlo,
     MCMC,
     MCSamples,
+    MCPaths,
     ISIntegrator,
     ISMC,
     ISMCMC,
@@ -23,4 +34,8 @@ export
     QuadIntegrator,
     GaussQuadrature,
     gaussquad,
-    gaussquad_2D
\ No newline at end of file
+    gaussquad_2D,
+    PathIntegrator,
+    RiemannIntegrator,
+    ItoIntegrator,
+    compute_integral
\ No newline at end of file
diff --git a/src/Integrators/monte_carlo.jl b/src/Integrators/monte_carlo.jl
index ea44993..65ef5d7 100644
--- a/src/Integrators/monte_carlo.jl
+++ b/src/Integrators/monte_carlo.jl
@@ -1,4 +1,4 @@
-abstract type MCIntegrator <: Integrator end
+abstract type MCIntegrator <: GibbsIntegrator end
 
 """
 struct MonteCarlo <: MCIntegrator
@@ -23,12 +23,12 @@ This method is implemented when the distribution cannot be analytically sampled.
 # Arguments
 - `n :: Int`               : number of samples
 - `sampler :: Sampler`     : type of sampler (see `Sampler`)
-- `ρ0 :: Distribution`     : prior distribution of the state
+- `ρ0 :: Union{Distribution, Real, Vector{<:Real}}`     : initial state or prior distribution of the state
 """
 struct MCMC <: MCIntegrator
     n :: Int
     sampler :: Sampler
-    ρ0 :: Distribution
+    ρ0 :: Union{Distribution, Real, Vector{<:Real}}
 end
 
 
diff --git a/src/Integrators/quadrature.jl b/src/Integrators/quadrature.jl
index fe8a0be..809bf17 100644
--- a/src/Integrators/quadrature.jl
+++ b/src/Integrators/quadrature.jl
@@ -1,4 +1,4 @@
-abstract type QuadIntegrator <: Integrator end
+abstract type QuadIntegrator <: GibbsIntegrator end
 
 
 """