Related papers: On the differentiability of solutions of stochasti…

In the recent years there has been an increased interest in studying regularity properties of the derivatives of stochastic evolution equations (SEEs) with respect to their initial values. In particular, in the scientific literature it has…

In this article we develop a framework for studying parabolic semilinear stochastic evolution equations (SEEs) with singularities in the initial condition and singularities at the initial time of the time-dependent coefficients of the…

We close an unexpected gap in the literature of stochastic differential equations (SDEs) with drifts of super linear growth (and random coefficients), namely, we prove Malliavin and Parametric Differentiability of such SDEs. The former is…

Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity conditions on coefficients. Existence and uniqueness of the mild…

By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to…

In this paper we develop a new approach to stochastic evolution equations with an unbounded drift $A$ which is dependent on time and the underlying probability space in an adapted way. It is well-known that the semigroup approach to…

Using purely probabilistic methods, we prove the existence and the uniqueness of solutions fora system of coupled forward-backward stochastic differential equations (FBSDEs) with measurable, possibly discontinuous coefficients. As a…

A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…

In this paper we study the following non-autonomous stochastic evolution equation on a UMD Banach space $E$ with type 2, {equation}\label{eq:SEab}\tag{SE} {{aligned} dU(t) & = (A(t)U(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), \quad t\in [0,T],…

In this article we show that a finite dimensional stochastic differential equation driven by a L\'evy process can be formulated as a stochastic partial differential equation. We prove the existence and uniqueness of strong solutions of such…

In Rajeev (2013), 'Translation invariant diffusion in the space of tempered distributions', it was shown that there is an one to one correspondence between solutions of a class of finite dimensional SDEs and solutions of a class of SPDEs in…

We consider semilinear evolution equations of the form $a(t)\partial_{tt}u + b(t) \partial_t u + Lu = f(x,u)$ and $b(t) \partial_t u + Lu = f(x,u),$ with possibly unbounded $a(t)$ and possibly sign-changing damping coefficient $b(t)$, and…

We consider parabolic PDEs associated with fractional type operators drifted by non-linear singular first order terms. When the drift enjoys some boundedness properties in appropriate Lebesgue and Besov spaces, we establish by exploiting a…

We prove the existence and uniqueness of solutions of degenerate linear stochastic evolution equations driven by jump processes in a Hilbert scale using the variational framework of stochastic evolution equations and the method of vanishing…

This paper presents a novel approach to rigorously solving initial value problems for semilinear parabolic partial differential equations (PDEs) using fully spectral Fourier-Chebyshev expansions. By reformulating the PDE as a system of…

We study fully nonlinear second-order (forward) stochastic partial differential equations (SPDEs). They can also be viewed as forward path-dependent PDEs (PPDEs) and will be treated as rough PDEs (RPDEs) under a unified framework. We…

We survey some of our recent results on existence, uniqueness and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random…

In this article we establish regularity properties for solutions of infinite dimensional Kolmogorov equations. We prove that if the nonlinear drift coefficients, the nonlinear diffusion coefficients, and the initial conditions of the…

Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…

We prove existence and uniqueness of solutions to a class of stochastic semilinear evolution equations with a monotone nonlinear drift term and multiplicative noise, considerably extending corresponding results obtained in previous work of…