What do you mean by "brick ceiling walls"? Brick ceiling and walls? Why do the walls shake if they are masonry? The best way to insulate from noise is to install resilient channels and attach sonopanels to the underside of the channels and then drywall. However, if this is a rental, I doubt the landlord would approve.

If this is an apartment, you probably don't have the ability to make structural changes. Unless being in Europe your terminology is different—here in the US an apartment is generally owned by someone else. Maybe in Europe you can own your own.

@Huesmann In some countries in Europe it is not unusual to own an apartment in a larger complex. In most cases there is a owners association or something similar which sets standards for the whole complex, which usually includes limits on what you can do in renovations. (They also handle maintenance of common areas like hallways and elevators.) In most countries, passive membership of that association (and paying membership fees) is mandatory for all inhabitants of the complex. If you don't like their rules you will have to propose a change and convince the other home-owners to accept it.

@Huesmann I guess so. I'm no that familiar with condo's, but they appear to operate along the same lines as far as I can tell.

Several answers show that DIY is unlikely to be successful. I suggest you consider a legal approach: Complain to your landlord (if renting); investigate your country's noise abatement laws; speak to a lawyer; or post on law.stackexchange.com if you are prepared to publish your country.

If there are other tenants/neighbours, talk to them and get them to complain to the landlord too. It may be worth considering whether its time to move, if the landlord approach doesn't work.

@PeterBill why go straight to litigation? Why not try talking with the upstairs neighbour first and see if they are aware of the sound transmission level in the building and perhaps they can curb their behaviour?

I was sarcastically going to say eliminate the kids... An other alternative perhaps depending on your building is to swap apartments with them. When I was a kid we had a grandfather clock on the common wall of our duplex. It chimed every 15 minutes to some degree. We did not find out until a couple of years later when the neighbours were over for dinner that they could hear the clock when it went off (OOPS). We set the clock to silent mode after that. That being said, talk with your neighbours first and see what can be done.

Others have commented about installing carpet. In my current Apt style condo, it is a 3 story wood frame construction. I am on the ground floor. I can hear the conversations of people in the unit above me (they are not yelling). I can hear the small dog on the 3rd floor that never stops barking it seems. My board is VERY aware of the sound issue and it is mandated that that all flooring be carpeted with the exception of Kitchen and Bathroom. I will go a step further and say make sure you get underlayment for the carpeting. The softer and thicker that carpet is, the more vibs it absorbs.

@Huesmann In Europe its common to mix renting and owning in a single building. Renters will often rent from landlords who own single apartments within the buildings in the same way as an owner occupier. So the distinction between condo/apartment doesn't really exist in the same way. That seems to mostly be a US thing.

@ForwardEd the law in both Europe and the US explicitly excludes noises made by children from quiet time regulations. And, no, parenting alone isn't sufficient to stop loud kids in all cases, there's always exceptions.

@user1937198 that sounds to me just like condo owners renting out their unit(s) in a building.

@JonathanReez Well, children's noise must be tolerated, but within limits. Especially the night times between 10 pm and 6 am are to be quiet. Additionally, even though the children can play, their noise still diminishes the value of the apartment and the quality of life thee, which may warrant a rent reduction (if the place is rented).

I would talk to the neighbors and try to come to an arrangement that caters a bit to your habits: The children can play in the rooms where you probably are not at the given time of day/weekday. E.g., during home office it's best if they are above your sleep room, but at night the other way around.

@Peter-ReinstateMonica as per my understanding there are no limits as long as the parents aren’t being malicious and the noise is purely a result of children’s voices or running around, rather than them playing music instruments or blasting YouTube from loudspeakers. You could certainly talk to the neighbors but don’t be angry if the parents warily tell you they’re well aware but have a hard time dealing with the issue.

@JonathanReez "Ihr Spielen darf aber nicht zu einer unzumutbaren Störung anderer Hausbewohner führen. Darauf müssen Eltern, insbesondere während der allgemeinen Ruhezeiten – mittags von 13 bis 15 Uhr und abends ab 22 Uhr bis zum nächsten Morgen 7 Uhr -, achten."

@Peter-ReinstateMonica However, the laughter, weeping and shouting of small children must be accepted by every resident as a natural behaviour of the children (AG Bergisch Gladbach WuM 83, 236; AG Aachen WuM 75, 38), as well as the rest that arises as a result of the normal children's play or movement instinct. It depends on the exact details but generally speaking OP would have a very hard time getting the police involved.

@JonathanReez Sure. But after 10 p.m. the parents should reign them in. In rental apartments one would involve the landlord and possibly reduce the rent; in an apartment owner's situation, one would likely ask the court for an... order? Injunction? Rather not the police.

@Peter-ReinstateMonica re: your landlord, sure, you could try to negotiate it. As for the courts, I would be extremely surprised if you'd be successful assuming the children are reasonably young and there's no abuse involved.