On threshold autoregressive processes
On trajectories of Gaussian Markov random fields
On transformations of Wiener space.
On transience conditions for Markov chains and random walks.
On Truncated Variation of Brownian Motion with Drift
We introduce the concept of truncated variation of Brownian motion with drift, which differs from regular variation by neglecting small jumps (smaller than some c > 0). We estimate the expected value of the truncated variation. The behaviour resembling phase transition as c varies is revealed. Truncated variation appears in the formula for an upper bound for return from any trading based on a single asset with flat commission.
On two fragmentation schemes with algebraic splitting probability
Consider the following inhomogeneous fragmentation model: suppose an initial particle with mass x₀ ∈ (0,1) undergoes splitting into b > 1 fragments of random sizes with some size-dependent probability p(x₀). With probability 1-p(x₀), this particle is left unchanged forever. Iterate the splitting procedure on each sub-fragment if any, independently. Two cases are considered: the stable and unstable case with and respectively, for some a > 0. In the first (resp. second) case, since smaller...
On unequally spaced AR(1) process
Discrete autoregressive process of the first order is considered. The process is observed at unequally spaced time instants. Both least squares estimate and maximum likelihood estimate of the autocorrelation coefficient are analyzed. We show some dangers related with the estimates when the true value of the autocorrelation coefficient is small. Monte-Carlo method is used to illustrate the problems.
On valuation of derivative securities: A Lie group analytical approach
This paper proposes a Lie group analytical approach to tackle the problem of pricing derivative securities. By exploiting the infinitesimal symmetries of the Boundary Value Problem (BVP) satisfied by the price of a derivative security, our method provides an effective algorithm for obtaining its explicit solution.
On Vector Measures Related to Deterministic Non-Stationary Stochastic Processes.
On vector-valued Hardy martingales and a generalized Jensen's inequality.
On Vershik's standardness criterion and Tsirelson's notion of cosiness
On Wald's equation. Discrete time case
On Walsh's brownian motions
On weak brownian motions of arbitrary order
On weak convergence of sequences of continuous local martingales
On Weak Convergence Of Spectral Density Estimate
On Weak Convergence of Stochastic Processes With Lusin Path Spaces.
On Weak Tail Domination of Random Vectors
Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular then weak tail domination implies strong tail domination. In particular, a positive answer to Oleszkiewicz's question would follow from the so-called Bernoulli conjecture. We also prove that any unconditional logarithmically concave distribution is strongly dominated by a product symmetric exponential measure.
On weakly measurable stochastic processes and absolutely summing operators
A characterization of absolutely summing operators by means of McShane integrable stochastic processes is considered.
On Wiener–Hopf factors for stable processes
We give a series representation of the logarithm of the bivariate Laplace exponent κ of α-stable processes for almost all α ∈ (0, 2].