Related papers: Discrete It\^o Formulas and Their Applications to …
In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional It\^{o} model when the discrete rebalancing dates are stopping times. We investigate the convergence,…
This paper introduces the path derivatives, in the spirit of Dupire's functional It\^o calculus, for the controlled paths in the rough path theory with possibly non-geometric rough paths. The theory allows us to deal with rough integration…
These notes contains an introduction to the theory of Brownian and diffusion local time, as well as its relations to the Tanaka Formula, the extended Ito-Tanaka formula for convex functions, the running maximum process, and the theory of…
We prove strong existense of solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey class type.
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
Processes which arise as solutions to stochastic differential equations involving the local time (SDELTs), such as skew Brownian motion, are frequent sources of inspiration in theory and applications. Existence and uniqueness results for…
Symmetry methods are by now recognized as one of the main tools to attack deterministic differential equations (both ODEs and PDEs); the situation is quite different for what concerns stochastic differential equations: here, symmetry…
We consider a discrete time analog of $G$--expectations and we prove that in the case where the time step goes to 0 the corresponding values converge to the original $G$--expectation. Furthermore we provide error estimates for the…
We survey the classical results of the Dirichlet Approximation Theorem.
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
We study the approximation of certain stochastic integrals with respect to a d-dimensional diffusion by corresponding stochastic integrals with piece-wise constant integrands. In finance this corresponds to replacing a continuously adjusted…
We consider a Markov process $X$ associated to a nonnecessarily symmetric Dirichlet form $\mathcal{E}$. We define a stochastic integral with respect to a class of additive functionals of zero quadratic variation and then we obtain an…
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class…
This paper provides an existence-and-uniqueness theorem characterizing the stochastic integral with respect to a Wiener process. The integral is represented as a mapping from the space of measurable and adapted pathwise locally integrable…
The `local time on curves' formula of Peskir provides a stochastic change of variables formula for a function whose derivatives may be discontinuous over a time-dependent curve, a setting which occurs often in applications in optimal…
We study the local (in time) expansion of a continuous-time process and its conditional moments, including the process' characteristic function. The expansions are conducted by using the properties of the (time-extended) Ito signature, a…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
Given strong uniqueness for an It\^o's stochastic equation, we prove that its solution can beconstructed on "any" probability space by using, for example, Euler's polygonal approximations. Stochastic equations in $\mathbb{R}^{d}$ and in…
A generalized It${\hat {\rm o}}$ formula for time dependent functions of two-dimensional continuous semi-martingales is proved. The formula uses the local time of each coordinate process of the semi-martingale, left space and time first…
The note provides the relation between symmetries and first integrals of It\^{o} stochastic differential equations and symmetries of the associated Kolmogorov backward equation. Relation between the symmetries of the Kolmogorov backward…