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Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The case of transmission (interface) boundary…
The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be…
We solve the Skorokhod embedding problem for a class of Gaussian processes including Brownian motion with non-linear drift. Our approach relies on solving an associated strongly coupled system of Forward Backward Stochastic Differential…
We construct Skorokhod decompositions for diffusions with singular drift and reflecting boundary behavior on open subsets of $\mathbb R^d$ with $C^2$-smooth boundary except for a sufficiently small set. This decomposition holds almost…
The objective of this article is to prove existence and weak uniqueness of a Walsh spider diffusion process, whose spinning measure and coefficients are allowed to depend on the local time spent at the junction vertex. The methodology is to…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
In this paper, we study ergodic backward stochastic differential equations (EBSDEs for short), for which the underlying diffusion is assumed to be multiplicative and of at most linear growth. The fact that the forward process has an…
The standard small-time functional central limit theorem of semimartingales has been established in (Gerhold, S., Kleinert, M., Porkert, P., and Shkolnikov, M. (2015). Small time central limit theorems for semimartingales with applications.…
In this paper, we establish a general convergence theorem for solutions of multivariate stochastic differential equations with countably many singular terms expressed as integrals with respect to local times. The processes under…
The deterministic Skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection. In the form studied here, the multidimensional Skorohod problem was introduced, in time-independent domains,…
We consider the surface Stokes equation with Lagrange multiplier and approach it numerically. Using a Taylor-Hood surface finite element method, along with an appropriate estimate for the additional Lagrange multiplier, we derive a new…
We consider a general one-dimensional overdamped diffusion model described by the It\^{o} stochastic differential equation (SDE) ${dX_t=\mu(X_t,t)dt+\sigma(X_t,t)dW_t}$, where $W_t$ is the standard Wiener process. We obtain a specific…
We propose and analyze a space-time Local Discontinuous Galerkin method for the approximation of the solution to parabolic problems. The method allows for very general discrete spaces and prismatic space-time meshes. Existence and…
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…
We study a time-inconsistent singular stochastic control problem for a general one-dimensional diffusion, where time-inconsistency arises from a non-exponential discount function. To address this, we adopt a game-theoretic framework and…
We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
In this work, we revisit the discrete-time Schr\"{o}dinger Bridge (SB) and Density Steering (DS) problems for Gaussian mixture model (GMM) boundary distributions. Building on the existing literature, we construct a set of feasible Markovian…
We prove that the standard conditions that provide unique solvability of a mixed stochastic differential equations also guarantee that its solution possesses finite moments. We also present conditions supplying existence of exponential…
The Smoluchowski equation with a time dependent sink term is solved exactly. In this method by knowing the probability distribution at the origin P(0,s), one may derive the probability distribution at all positions i.e., P(x,s). Further the…