Related papers: Skorohod and Stratonovich integrals for controlled…
This paper deals with asymptotic stability of a class of dynamical systems in terms of smooth Lyapunov pairs. We point out that well known converse Lyapunov results for differential inclusions cannot be applied to this class of dynamical…
We derive functional convergence of the partial maxima stochastic processes of multivariate linear processes with weakly dependent heavy-tailed innovations and random coefficients. The convergence takes place in the space of…
The paper is devoted to the existence of integral functionals $\int_0^\infty f(X(t))\,{\mathrm{d}t}$ for several classes of processes in $\mathbb{R}$ with $d\ge 3$. Some examples such as Brownian motion, fractional Brownian motion, compound…
In this paper, based on the white noise analysis of square integrable pure-jump Levy process given by [1], we define the formal derivative of fractional Levy process defined by the square integrable pure-jump Levy process as the fractional…
For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which evolves the variable of the orthogonal…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
Consider a stochastic process $\{X(t)\}$ on a finite state space $ {\sf X}=\{1,\dots, d\}$. It is conditionally Markov, given a real-valued `input process' $\{\zeta(t)\}$. This is assumed to be small, which is modeled through the scaling,…
Performing an nonperturbative path integral for the geometric part of a large class of 2d theories without kinetic term for the dilaton field, the quantum effects from scalar matter fields are treated as a perturbation. When integrated out…
Recently, doubts have been cast on the validity of the continuous-time coherent state path integral. This has led to controversies regarding the correct way of performing calculations with path integrals, and to several alternative…
We provide an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove that all Gromov-Witten classes of all smooth complete…
In this paper, we first analyze the strong and weak convergence of projective integration methods for multiscale stochastic dynamical systems driven by $\alpha$-stable processes, which are used to estimate the effect that the fast…
We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the…
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to L{\'e}vy processes in the Skorokhod space…
The paper is devoted to the integral functionals $\int_0^\infty f(X_t)\,{\mathrm{d}t}$ of Markov processes in $\X$ in the case $d\ge 3$. It is established that such functionals can be presented as the integrals $\int_{\X} f(y) \G(x,…
This paper is concerned with numerical analysis of two fully discrete Chorin-type projection methods for the stochastic Stokes equations with general non-solenoidal multiplicative noise. The first scheme is the standard Chorin scheme and…
We study a system of Skorokhod stochastic differential equations (SDEs) modeling the pairwise dispersion (in spatial dimension $d=2$) of heavy particles transported by a rough self-similar, turbulent flow with H\"{o}lder exponent $h\in…
This thesis presents two descriptions of complexity in dynamical systems. The algebraic approach deals with the differential Galois group theory and its restrictions on integrability. The geometric part is a formulation of dynamics in the…
We consider stochastic differential equations of the form $dY_t=V(Y_t)\,dX_t+V_0(Y_t)\,dt$ driven by a multi-dimensional Gaussian process. Under the assumption that the vector fields $V_0$ and $V=(V_1,\ldots,V_d)$ satisfy H\"{o}rmander's…
We solve the Skorokhod embedding problem for a class of stochastic processes satisfying an inhomogeneous stochastic differential equation (SDE) of the form $d A_t =\mu (t, A_t) d t + \sigma(t, A_t) d W_t$. We provide sufficient conditions…
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…