# PDEs of Mathematical Physics, A Modern Introduction IV - "Stochastic processes and PDEs in Mathematical Biology"

GFM seminar

IIIUL, Room B1-01

2013-07-09 14:30
2013-07-09 15:30
2013-07-09
14:30
..
15:30

Nico Stollenwerk (CMAF, Universidade de Lisboa)

We show stochastic processes in population biology, which naturally are linked to PDE descriptions, like the dynamics of generating and characteristic functions, Fokker-Planck approximations etc. Some of the simplest PDEs can be solved

explicitly giving probability distributions in time. The solutions can also be used to construct likelihood functions for data analysis via likelihood functions. Finally we show spatially extended stochastic processes and approximations of these as PDEs. In population biology such PDEs can be formulated as superdiffusive processes, using fractional derivatives for the Laplace

operators of the diffusion, describing fast spreading of e.g. diseases or long range animal movement.

explicitly giving probability distributions in time. The solutions can also be used to construct likelihood functions for data analysis via likelihood functions. Finally we show spatially extended stochastic processes and approximations of these as PDEs. In population biology such PDEs can be formulated as superdiffusive processes, using fractional derivatives for the Laplace

operators of the diffusion, describing fast spreading of e.g. diseases or long range animal movement.