We study the existence and the regularity of the local time of filtered white noises . We will also give Chung’s form of the law of iterated logarithm for , this shows that the result on the Hölder regularity, with respect to time, of the local time is sharp.
We study logarithmic estimates for a class of Fourier multipliers which arise from a nonsymmetric modulation of jumps of Lévy processes. In particular, this leads to corresponding tight bounds for second-order Riesz transforms on .
We consider a non-consuming agent interested in the maximization of the long-run growth rate of a wealth process investing either in a money market and in one risky asset following a geometric Brownian motion or in futures following an arithmetic Brownian motion. The agent faces proportional transaction costs, and similarly as in [17] where the case of stock trading is considered, we show how the log-optimal optimal policies in the long run can be derived when using the technical tool of shadow...
This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.
Let be a locally compact non-compact metric group. Assuming that is abelian we construct symmetric aperiodic random walks on with probabilities of return to any neighborhood V of the neutral element decaying at infinity almost as fast as the exponential function n ↦ exp(-n). We also show that for some discrete groups , the decay of the function can be made as slow as possible by choosing appropriate aperiodic random walks Sₙ on .
In this paper, we are interested in a diffusion process based on a gradient descent. The process is non Markov and has a memory term which is built as a weighted average of the drift term all along the past of the trajectory. For this type of diffusion, we study the long time behaviour of the process in terms of the memory. We exhibit some conditions for the long-time stability of the dynamical system and then provide, when stable, some convergence properties of the occupation measures and of the...